Solve Constant Alpha's in Images: Help to Understand and Get Unstuck

[yakin]

The book answer is 1, 3 and -2. I can't figure how they got it? Please help to understand and help me to get through where i got stuck.

Please look at images from bottom page to top page(where you see crossing on a page)

 

[MarkFL]

You have correctly found that the characteristic root is $r=-1$ of multiplicity 3, however, you have not properly dealt with the fact that the root is repeated. Since this root is of multiplicity 3, the closed-form will be:

\(\displaystyle a_n=c_1(-1)^n+c_2n(-1)^n+c_3n^2(-1)^n=(-1)^n\left(c_1+c_2n+c_3n^2 \right)\)

 

[yakin]

Thank you for your feedback. I noticed that. I forgot to stick "n" in the general form of the solution with the repeated roots. Thanks though!

Question: How do you write maths directly with correct notation here? I have to take pics of my work and then upload the pics.

 

[MarkFL]

...
Question: How do you write maths directly with correct notation here? I have to take pics of my work and then upload the pics.

We have $\LaTeX$ implemented here to allow writing mathematical expressions.

Here is a link to a thread containing a pdf tutorial written by one of our staff:

http://mathhelpboards.com/latex-tips-tutorials-56/math-help-boards-latex-guide-pdf-1142.html

 

[blue_raver22]

Hello,

I understand that you are having trouble understanding how to solve Constant Alpha's in images and how to get unstuck. I will do my best to explain the solution and help you understand it.

First, let's define Constant Alpha's. Constant Alpha's refer to a set of numbers that are multiplied by a variable in an image. In other words, they are constants that are multiplied by a variable in an image.

Now, let's look at the solution provided in the book, which is 1, 3, and -2. These numbers refer to the constants that are being multiplied by a variable in the image. In order to understand how these numbers were obtained, we need to look at the images from bottom page to top page.

When we look at the bottom page, we see that there is a number that is being multiplied by a variable. This number is referred to as the constant alpha. In this case, the constant alpha is 1. Moving up to the next page, we see that there is another constant alpha, which is 3. Finally, when we reach the top page, we see that there is a constant alpha of -2.

To get unstuck, you need to understand that these numbers are constants that are being multiplied by a variable in the image. By looking at the images from bottom page to top page, we can identify the constant alpha's and solve the problem.

I hope this explanation helps you understand and get through where you were stuck. If you have any further questions, please do not hesitate to ask. Good luck!